The mimetic finite difference discretization of diffusion problem on unstructured polyhedral meshes

Authors:
Konstantin Lipnikov;Mikhail Shashkov;Daniil Svyatskiy
Affiliations:
Los Alamos National Laboratory, MS B284, Los Alamos, NM 87545, United States;Los Alamos National Laboratory, MS B284, Los Alamos, NM 87545, United States;Department of Mathematics, University of Houston, 651 PGH, Houston, TX 77204, United States
Venue:
Journal of Computational Physics
Year:
2006

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Abstract

We study the mimetic finite difference discretization of diffusion-type problems on unstructured polyhedral meshes. We demonstrate high accuracy of the approximate solutions for general diffusion tensors, the second-order convergence rate for the scalar unknown and the first order convergence rate for the vector unknown on smooth or slightly distorted meshes, on non-matching meshes, and even on meshes with irregular-shaped polyhedra with flat faces. We show that in general the meshes with non-flat faces require more than one flux unknown per mesh face to get optimal convergence rates.